MAG-Bench: Multi-Domain Magnetic Benchmarking

• MAG-Bench is a comprehensive framework that standardizes benchmarking across MHD simulation validation, quantum magnetometer calibration, and ab initio magnetic structure prediction.
• It employs rigorous protocols—such as mesh convergence, magnetic shielding metrics, and configuration overlap—to ensure reproducible, quantitative evaluations.
• MAG-Bench drives advancements in fusion design, quantum sensing, and computational magnetism while highlighting challenges and pathways for future improvements.

MAG-Bench designates a precise and systematic benchmarking approach or physical platform in three distinct areas of contemporary magnetism and magnetic fusion research. In published literature, the term “MAG-Bench” has been employed to refer to: (i) a validation benchmark suite for magnetohydrodynamics (MHD) simulation codes used in magnetically driven inertial confinement fusion (ICF) design; (ii) a benchtop magnetic shielding and active-field-control testbed for the calibration of quantum magnetometers; and (iii) a high-throughput, cluster-multipole-theory-based computational framework for ab initio prediction and benchmarking of magnetic structures in solid state systems. Each domain of application is characterized by rigorous protocols and performance standards to enable reproducible and quantitative evaluation of either code output, device metrics, or computational prediction.

1. MAG-Bench in Magnetically Driven Inertial Confinement Fusion

MAG-Bench, as defined in the context of ICF modeling, is a structured suite of six experimental and theoretical benchmarks used to validate the multi-physics FLASH radiation-MHD code for predictive ICF target design (Ellison et al., 14 Apr 2025). Each benchmark encapsulates a different aspect of magnetically driven target physics, ranging from linear instability growth to scaling to ignition-relevant facilities.

The six benchmarks are:

1. Single-Mode Magneto–Rayleigh–Taylor (MRT) Growth: Focuses on the liner’s response to a prescribed, single-wavelength sinusoidal perturbation under intense current drive, with flash-matched mode growth to within 10% of experiment and synthetic radiography used as the figure of merit.
2. Multi-Mode MRT: Assesses response to surface imperfections/randomized initial conditions, emphasizing stochastic-seeded nonlinear instability and close morphological and spectral agreement with experimental radiographs for optimal perturbation amplitude selection.
3. Single-Mode Richtmyer–Meshkov (RMI) Growth: Treats shock-driven perturbative growth at material interfaces, validating shock position, interface trajectory, and amplitude scaling against experimental data and photonic velocity measurements.
4. ICF Confinement Time Platform: Benchmarks the code’s reproduction of 1D and 2D stagnation, confinement radii, and stagnation time in moderate-convergence beryllium liners filled with D₂, with validation via X-ray and velocity probe diagnostics.
5. Fully Integrated MagLIF Shot: Simulates full-coupling of laser preheat, axial magnetization, multi-group radiation, fusion reaction, and circuit drive, with output neutron yield and ion temperature matching experimental MagLIF data and reference LASNEX simulations within experimental and systematic uncertainties.
6. Current Scaling to 60 MA: Encodes scaling laws for geometric, material, and circuit attributes to preserve key dimensionless numbers at increased drive current, demonstrating flash/hydra consistency in implosion dynamics, fusion yield scaling, and ignition threshold.

Each benchmark is decomposed along seven descriptive axes: physical scenario, governing equations, theoretical scalings, FLASH code setup, experiment–simulation comparison, uncertainty/discrepancy assessment, and ICF design implications. The protocol explicitly ensures mesh convergence, error quantification, and physical fidelity, establishing FLASH/MAG-Bench as a standard for code-to-experiment-and-theory validation in pulsed-power fusion environments (Ellison et al., 14 Apr 2025).

2. MAG-Bench for Quantum Magnetometer Calibration

In atomic and quantum magnetometry, MAG-Bench denotes a standardized, benchtop-scale magnetic shielding enclosure with integrated internal field coils, designed for rigorous and reproducible magnetometer benchmarking (Hobson et al., 2022). The platform consists of:

• A four-layer, nested, μ-metal shield geometry optimized for axial and transverse shielding efficiency (SE), reaching SE_A(0.2 Hz) ≈ (1.0±0.1) × 10⁶ and SE_T(0.2 Hz) ≈ (20.2±0.1) × 10⁶, respectively. The shield employs high-permeability mumetal and custom spacing determined by a multi-objective genetic algorithm.
• Nine internal flexible-printed-circuit-board (fPCB) coils capable of producing three independent uniform fields, five linear gradients, and one quadratic gradient. Field uniformity and gradient linearity are maintained to ≤0.5% and ≤4% error over the central ≈150 mm cylindrical region, validated by optical-pumping magnetometer (OPM) mapping.
• An active nulling system leveraging in situ OPM mapping and least-squares coil current optimization to minimize static residual fields to <0.23 nT, a 19.5–19.8× reduction relative to pre-nulling values.
• Johnson (thermal) noise measurements demonstrating sub-15 fT/√Hz field noise at frequencies down to 10 Hz, below current OPM sensor noise floors.

The MAG-Bench protocol encompasses degaussing, frequency-resolved SE measurement, static-field profiling, coil calibration, active nulling, and residual noise characterization. The platform functions as a reproducible “standard” for evaluating the performance of prototype and next-generation quantum magnetometers, with key metrics including field noise floor, field uniformity, gradient accuracy, and static nulling efficacy (Hobson et al., 2022).

Table 1: Representative MAG-Bench Performance Metrics for Magnetometer Benchmarking

Metric	Value (Central Region)
Passive Shielding (SE_A)	(1.0±0.1) × 10⁶ @ 0.2 Hz
Field Uniformity	≤0.5% deviation
Gradient Linearity	≤4% error
Residual Static Field	≤0.23 nT (after nulling)
Magnetic Noise Floor	<15 fT/√Hz (10–100 Hz)

MAG-Bench in this context enables controlled, conventionalized comparison of OPM, NV-center, or other quantum magnetometer prototypes, facilitating device benchmarking under ultra-low-noise, well-characterized ambient field conditions.

3. MAG-Bench: Cluster-Multipole Theory and Ab Initio Magnetic Structure Benchmarking

In computational condensed matter physics, MAG-Bench refers to a high-throughput pipeline for ab initio magnetic structure prediction and benchmarking, utilizing the cluster-multipole (CMP) expansion formalism and direct comparison with experimental data from MAGNDATA (Huebsch et al., 2020). The approach comprises:

• Generation of an exhaustive, symmetry-dictated basis of zero-q magnetic configurations (collinear and noncollinear) via CMP expansion adapted to the crystallographic point group. Each candidate structure is represented as a linear combination of a minimal set of orthonormal CMPs.
• Construction of candidate lists for each material, including “additional guesses” (linear combinations of same-order CMPs) known to capture experimentally observed mixed multipole states.
• Automated execution of spin-density functional theory (SDFT + SOC, in VASP) calculations for all candidates, followed by clustering of the results to identify distinct local minima.
• Direct comparison to experimental magnetic structures using configuration overlap ($O$), ground-state matching (magnetic space group), and on-site moment size error ($\delta\mu$).

Table 2: MAG-Bench Computational Benchmark Success Rates (MAGNDATA q=0 Compounds)

Metric	d-orbital	f-orbital	Total
$O_{fin,exp} > 0.75$	87.6%	64.0%	82.8%
mspg match in any minimum	96.9%	60.0%	89.3%
Mean absolute error in $\mu$ ($\mu_B$)	–	–	≈0.5 μ_B
Global min with correct mspg (CMP+SDFT)	43.3%	12.0%	36.9%

For d-electron materials, the local minimum most similar to experiment lies within 1 meV/degree of freedom of the computed global minimum in ≈77.7% of cases, typically reducing the search space to ≈4.5 magnetic candidates. The predictive margin for f-electron materials is less robust, reflecting outstanding challenges in SDFT for strongly correlated electrons and partial moment cancellation (Huebsch et al., 2020).

No improvement is achieved by introducing on-site Hubbard-U corrections to SDFT for ground-state structure prediction; both the set of predicted local minima and agreement with experiment remain statistically unchanged for the tested parameter range. The protocol applies only to commensurate (q=0) orders but may be extended, in principle, to multi-q and incommensurate states by enlargement of the unit cell.

4. Protocols, Metrics, and Standardization

All MAG-Bench incarnations are defined by rigorous procedures—experimental, theoretical, or computational—intended to ensure that comparisons are quantitative, reproducible, and physically meaningful.

• Fusion simulation MAG-Bench: Seven-stage descriptions per benchmark (geometry, equations, scaling, setup, results, uncertainty, implications), strict mesh and error convergence, side-by-side experiment/theory/code comparison.
• Magnetometer test-bed MAG-Bench: Stepwise protocol from degaussing through nulling, with performance summarized via quantifiable SE, uniformity, residual field, and noise metrics, enabling standardized cross-laboratory evaluation.
• Ab initio MAG-Bench: Well-defined CMP/SDFT workflow, energy ranking, overlap, and on-site moment accuracy metrics, with results referenced explicitly to experimental ground truth.

The unifying property is the creation of a “benchmarking environment” for either numerical code, physical sensor, or structural prediction algorithm, with clearly specified physical parameters, figures of merit, and uncertainty quantification.

5. Impact, Limitations, and Future Directions

MAG-Bench benchmarks underpin confidence in simulation-driven design for fusion targets, high-sensitivity field measurements, and computational magnetic structure discovery.

• ICF/MHD: Validated code performance enables design extrapolation to Pacific Fusion's 60 MA Demonstration System and facility-gain-scale MagLIF. Future recommendations include advanced alpha-transport modeling, full uncertainty quantification, and EOS refinements (Ellison et al., 14 Apr 2025).
• Quantum magnetometry: Standardized testbed protocols promote reproducible device comparison, calibration routine optimization, and benchmarking under standardized low-noise, low-remanence conditions; extension to cryogenic operation and alternative sensor modalities is plausible (Hobson et al., 2022).
• Ab initio magnetic structure: MAG-Bench enables reduction of the vast configurational space in magnetic oxides/intermetallics to tractable, symmetry-motivated candidates, offering ∼0.5 μ_B predictive accuracy for on-site moments. Noted limitations include lack of magnetostructural relaxation, restrictions to q=0 structures, and suboptimal performance for strongly correlated f-electron systems. Future improvements point to advanced exchange–correlation functionals, SDFT+DMFT, and expansion to multi-q orders (Huebsch et al., 2020).

A plausible implication is that, as further benchmark datasets become available, MAG-Bench-style platforms will be increasingly central to establishing best practices for complex, high-dimensional magnetic system evaluation—spanning theory, simulation, and precision experiment.